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Dean Harman is a professor of chemistry at the University of Virginia, where he has been honored with several teaching awards. He heads Harman Research Group, which specializes in the novel organic transformations made possible by electron-rich metal centers such as Os(II), RE(I), AND W(0). He holds a Ph.D. from Stanford University.

Gordon Yee is an associate professor of chemistry at Virginia Tech in Blacksburg, VA. He received his Ph.D. from Stanford University and completed postdoctoral work at DuPont. A widely published author, Professor Yee studies molecule-based magnetism.

Tarek Sammakia is a Professor of Chemistry at the University of Colorado at Boulder where he teaches organic chemistry to undergraduate and graduate students. He received his Ph.D. from Yale University and carried out postdoctoral research at Harvard University. He has received several national awards for his work in synthetic and mechanistic organic chemistry.

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Okay, so now we've introduced the concept of proton concentration, and we've introduced the concept of pH. Let's use those ideas and apply them to some real world systems. And it turns out to be extremely easy to calculate the proton concentration, and the hydroxide ion concentration, and pH and pOH for a subset of acids and bases, and that subset are the strong acids and the strong bases. What we're going to look at first is we're going to look at the monoprotic strong acids. And the monoprotic strong acids are HCl, HNO[3], hydrochloric acid, nitric acid, perchloric acid, hydrobromic acid, hydriodic acid, chloric acid. And we can represent what goes on when we take these and dissolve them into water as HX, where X represents the conjugate base of each one of these strong acids. So HX goes to H plus, plus X minus. And, of course, we know that H plus is the hydronium, so that this is a solvated proton. And the thing about strong acids, again, is that this happens to essentially 100 percent completion. So, in other words, if we start with 0.13 molar concentration of HX, so, say, nitric acid, then, because nitric acid is a strong acid, we can immediately say that the concentration of protons in solution is .13 molar, as well. Similarly, if we started with something like 5.2 times 10^-3 molar in HX - say this is hydrobromic acid - then that corresponds to 5.2 times 10^-3 molar proton concentration, as well. And again, we can only make these identities - so these numbers are exactly the same - because we're talking about a strong acid and, in particular, a strong monoprotic acid, meaning that there's only one acidic proton that we have to worry about.
So we could calculate, for instance, very trivially, what is the pH of a 6.8 times 10^-4 molar solution of hydrobromic acid. And, because HBr is a strong acid, we can immediately make the identity that the proton concentration is also 6.8 times 10^-4 molar. And so, the pH, which is negative log base 10 of the proton concentration is equal to this expression. Take the negative log of this, and we get 3.17. And I'll remind you that we express this to two decimal places past the decimal point, because there are two significant figures in our original concentration. So for monoprotic strong acids, really a trivial thing to do.
Now, for polyprotic strong acids, and the only one that we're going to be concerned with is sulfuric acid, you can't quite stop at this point. So you're really close and we'll see, when we talk about polyprotic acids, that we're really close. But we do have to consider, after that first association, which is complete - in other words, sulfuric acid is a strong acid - because this first step is 100 percent. But then there's an additional equilibrium, where bisulfate can further dissociate into a proton and sulfate, and we have to worry about that. So we will re-examine that when we look at the polyprotic acids. So, for right now, it's really easy to do monoprotic acids only, monoprotic strong acids.
Now, if we look at bases and, in particular, we're going to look at strong bases. The strong bases that give 1 equivalent to hydroxide when we dissolve them are things like lithium hydroxide, potassium hydroxide, sodium hydroxide, but also things like sodium hydride, which gives sodium, and hydroxide and half an equivalent of hydrogen gas. And we can make the exact same sort of identity that we could with the strong acids, which is that the concentration of hydroxide is exactly equal to the concentration of our original metal hydroxide that we put in solution. So, if we prepare a .35 molar solution of potassium hydroxide, we can immediately say that the concentration of hydroxide is .35 molar, as well. And again, this is because these things, lithium hydroxide, potassium hydroxide, completely dissociated when we throw them into water.
Okay, let's now take a look at a problem, keeping in mind that we can identify the hydroxide ion concentration with the original concentration of the alkali metal hydroxide that we put in solution. If we were asked to calculate, "What is the hydroxide ion concentration, the pOH and the pH, for a 0.43 molar solution of potassium hydroxide?", we could again immediately identify hydroxide concentration is equal to 0.43 molar. That means that the pOH, which is the negative log base 10 of the hydroxide ion concentration, is equal to 0.37, and the pH, which is 14.00 minus the pOH, equals 13.63. And again, this equation comes from the fact that pH plus pOH is equal to 14.00 at 25C.
Now, there's only a slight wrinkle when we look at things like alkaline earth hydroxides of the form M(OH)[2], and the reason is, for instance, with calcium hydroxide, that, when we dissolve calcium hydroxide into water, we get calcium cations, but we get two equivalents of hydroxide for every equivalent of calcium hydroxide we originally put into the pot. And so, if we were asked to calculate the pH of a 0.13 molar solution of calcium hydroxide, the hydroxide ion concentration in solution is going to be equal to 0.26 molar, which is twice what the original concentration of calcium hydroxide was. And from this, hydroxide ion concentration is equal to 0.26 molar, we can get that the proton concentration is 10^-14 divided by 0.26, which is equal to 3.8 times 10^-4, and pH is the negative log of this quantity, which is 13.41. And again, this is a highly alkaline solution, which makes sense, because we made up a solution that is about 10^th molar in a strong base.
Now finally, I need to say a word about solutions that have proton concentrations or hydroxide concentrations that are very small. And this applies to both strong acids and weak bases and strong bases and weak bases. And I'll introduce this idea by giving you a problem and showing you how to calculate it wrong. And that is, "What is the pH of a 10^-9 molar solution of hydrochloric acid?" And you might say, "Okay, well, HCl is a strong acid, therefore the proton concentration is equal to 10^-9, so we can immediately make that identity. And therefore the pH, which is negative log base 10 of this quantity, is 9." And what's wrong with that? Well, what's wrong with it is that your intuition tells you that, if you have a solution that's a solution of a strong acid, even it's a really, really, really dilute strong acid, it still shouldn't become alkaline. This says that the solution is alkaline, and that the pH is above 7, meaning that it's very basic. And that doesn't make intuitive sense. Well, what did we do wrong?
Well, we can't exactly answer the exact concentration of protons, but it's more right, certainly, to say that the proton concentration is approximately 10^-7, which is that due to self-ionization of water. Remember, water can be dissociated into protons and hydroxide. So we have that the proton concentration is roughly the sum of what's originally there and what we've added. Now, this is not an exact expression, but, at least semi-quantitatively, what it says is that the proton concentration is going to be ever so slightly higher than what it is in neutral water. That makes good sense, because we've added some acid. It's 10^-9 molar solution of HCl. The pH, if we calculated the pH, is going to be ever so slightly less than 7, and that makes more sense. It's clearly not 9. 9 would say that it's an alkaline solution. Something that's ever so slightly less than 7 fits with our intuition that the solution should be slightly acidic, based on the fact that we've added a little bit of hydrochloric acid.
Okay, so what have we talked about? We've shown that it's really easy to calculate proton concentrations in pH's and hydroxide ion concentrations in pOH's for strong acids and strong bases, with a couple of things to think about: 1) we haven't treated sulfuric acid, which is a diprotic acid, and we have to worry about that second ionization; for alkaline earth hydroxides, like calcium hydroxides, we have to worry a lot about the fact that you get 2 equivalents of hydroxide for every equivalent of calcium hydroxide you put into the pot. And finally, what we talked about is the fact that if you end up with really dilute solutions of protons as a result of adding acid or adding base, then you have to consider the self-ionization of water when you're doing your calculations. And, in any case, use your intuition. If your of a solution that should be acidic and the pH says that it's something above 7, then that doesn't make sense. So what you have to do is go back and reconsider the self-ionization of water as sort of an intrinsic proton concentration even in neutral water.
Acids and Bases
Acid and Base Strengths
Strong Acids and Bases Page [2 of 2]

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